Answer
The equation for the $n$th term is
$a_n=0.5(-6)^{n-1}$
and $a_6=-3888$
Work Step by Step
Write down the series from the graph.
$0.5,-3,18,-108,...$
First term $a_1=0.5$.
Common ratio $r=\frac{-3}{0.5}=-6$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $0.5$ for $a_1$ and $-6$ for $r$.
$\Rightarrow a_n=0.5(-6)^{n-1}$
Substitute $6$ for $n$.
$\Rightarrow a_6=0.5(-6)^{6-1}$
Simplify.
$\Rightarrow a_6=0.5(-6)^{5}$
$\Rightarrow a_6=-3888$.
